Consider a two player game where each player has $n$ cards numbered $1,2,\dots,n$ . On each turn both players place one of their cards on the table. The player who placed the higher card gets one point. If the cards are equal, neither player gets a point. The game continues until all cards have been played.
You are given the number of cards $n$ and the players' scores at the end of the game, $a$ and $b$ . Your task is to give an example of how the game could have played out.
The first line contains one integer $t$ : the number of tests.
Then there are $t$ lines, each with three integers $n$ , $a$ and $b$ .
For each test case print YES if there is a game with the given outcome and NO otherwise.
If the answer is YES , print an example of one possible game. Print two lines representing the order in which the players place their cards. You can give any valid example.
5 4 1 2 2 0 1 3 0 0 2 1 1 4 4 1\n · · \n · · \n · · \n · · \n · · \n
YES 1 4 3 2 2 1 3 4 NO YES 1 2 3 1 2 3 YES 1 2 2 1 NO\n · · · \n · · · \n \n \n · · \n · · \n \n · \n · \n \n